On the Existence and Disjunction Properties in Structural Set Theory
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909675123900416 |
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| author | Saving, Mark |
| author_facet | Saving, Mark |
| contents | We formulate a definition of the existence property that works with "structural" set theories, in the mode of ETCS (the elementary theory of the category of sets). We show that a range of structural set theories, when formulated using constructive logic, satisfy the disjunction, numerical existence, and existence properties; in particular, intuitionist ETCS, formulated with separation and Shulman's replacement of contexts axiom, satisfies these properties. As a consequence of this, we show that, working constructively, replacement of contexts is strictly weaker than collection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03717 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Existence and Disjunction Properties in Structural Set Theory Saving, Mark Logic Category Theory 03F50 (Primary) 03G30, 03E70 (Secondary) We formulate a definition of the existence property that works with "structural" set theories, in the mode of ETCS (the elementary theory of the category of sets). We show that a range of structural set theories, when formulated using constructive logic, satisfy the disjunction, numerical existence, and existence properties; in particular, intuitionist ETCS, formulated with separation and Shulman's replacement of contexts axiom, satisfies these properties. As a consequence of this, we show that, working constructively, replacement of contexts is strictly weaker than collection. |
| title | On the Existence and Disjunction Properties in Structural Set Theory |
| topic | Logic Category Theory 03F50 (Primary) 03G30, 03E70 (Secondary) |
| url | https://arxiv.org/abs/2312.03717 |